{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NZD2G5BPCFCBVU32EZM3YHWUZ4","short_pith_number":"pith:NZD2G5BP","canonical_record":{"source":{"id":"1701.01827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T13:22:00Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"f6601860629fdf61163c1a6d216ad8dc4ebf5d356359c7559eb3bda413819b29","abstract_canon_sha256":"4ce4564bf6902f6c5d452f3b1b7a246e42cd39ec4b0f013aecf1b16ed8991dce"},"schema_version":"1.0"},"canonical_sha256":"6e47a3742f11441ad37a2659bc1ed4cf03aa58632441a2c8817f94159b307905","source":{"kind":"arxiv","id":"1701.01827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01827","created_at":"2026-05-18T00:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01827v1","created_at":"2026-05-18T00:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01827","created_at":"2026-05-18T00:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"NZD2G5BPCFCB","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZD2G5BPCFCBVU32","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZD2G5BP","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NZD2G5BPCFCBVU32EZM3YHWUZ4","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T13:22:00Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"f6601860629fdf61163c1a6d216ad8dc4ebf5d356359c7559eb3bda413819b29","abstract_canon_sha256":"4ce4564bf6902f6c5d452f3b1b7a246e42cd39ec4b0f013aecf1b16ed8991dce"},"schema_version":"1.0"},"canonical_sha256":"6e47a3742f11441ad37a2659bc1ed4cf03aa58632441a2c8817f94159b307905","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:13.349444Z","signature_b64":"AXwmLrGLUNVpk863HIaMVsFw1iOtvHgeNHjICU/NXPRquWxtZnTl5GG+6zYpv2EZijwuWzbYYv5UBYhMkoPzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e47a3742f11441ad37a2659bc1ed4cf03aa58632441a2c8817f94159b307905","last_reissued_at":"2026-05-18T00:53:13.348745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:13.348745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01827","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPUbycfY4YyjIGnBs7GFLxSeAO5IZjDwuuU6+pip7NMYK//zVfUFBQlu9khWHysNdlGjqXA+EQejzjogWUmPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:32:48.431655Z"},"content_sha256":"75a99b4d6a39c7a2ca3bb0206ab84edaacb094ca34e2bb78c4b75098c3452be4","schema_version":"1.0","event_id":"sha256:75a99b4d6a39c7a2ca3bb0206ab84edaacb094ca34e2bb78c4b75098c3452be4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NZD2G5BPCFCBVU32EZM3YHWUZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On equivariant indices of 1-forms on varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Firuza I. Mamedova, Sabir M. Gusein-Zade","submitted_at":"2017-01-07T13:22:00Z","abstract_excerpt":"For a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group) one has notions of the equivariant homological index and of the (reduced) equivariant radial index as elements of the ring of complex representations of the group. We show that on a germ of a smooth complex-analytic G-variety these indices coincide. This permits to consider the difference between them as a version of the equivariant Milnor number of a germ a G-variety with an isolated singular point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01827","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/aXmdudkWEKrvjTd01FmabJlOVoOT3MU37mgXznplzeVYDTENBJTqSSG0dWUAWKhRl+YzejQ11DB69ip8JTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:32:48.431997Z"},"content_sha256":"46c818366b2307e6f87f5dac25d767e6b241304dd4a8fe4975bab27e5a7af345","schema_version":"1.0","event_id":"sha256:46c818366b2307e6f87f5dac25d767e6b241304dd4a8fe4975bab27e5a7af345"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4/bundle.json","state_url":"https://pith.science/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T15:32:48Z","links":{"resolver":"https://pith.science/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4","bundle":"https://pith.science/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4/bundle.json","state":"https://pith.science/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZD2G5BPCFCBVU32EZM3YHWUZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NZD2G5BPCFCBVU32EZM3YHWUZ4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4ce4564bf6902f6c5d452f3b1b7a246e42cd39ec4b0f013aecf1b16ed8991dce","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T13:22:00Z","title_canon_sha256":"f6601860629fdf61163c1a6d216ad8dc4ebf5d356359c7559eb3bda413819b29"},"schema_version":"1.0","source":{"id":"1701.01827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01827","created_at":"2026-05-18T00:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01827v1","created_at":"2026-05-18T00:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01827","created_at":"2026-05-18T00:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"NZD2G5BPCFCB","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NZD2G5BPCFCBVU32","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NZD2G5BP","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:46c818366b2307e6f87f5dac25d767e6b241304dd4a8fe4975bab27e5a7af345","target":"graph","created_at":"2026-05-18T00:53:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group) one has notions of the equivariant homological index and of the (reduced) equivariant radial index as elements of the ring of complex representations of the group. We show that on a germ of a smooth complex-analytic G-variety these indices coincide. This permits to consider the difference between them as a version of the equivariant Milnor number of a germ a G-variety with an isolated singular point.","authors_text":"Firuza I. Mamedova, Sabir M. Gusein-Zade","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T13:22:00Z","title":"On equivariant indices of 1-forms on varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01827","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:75a99b4d6a39c7a2ca3bb0206ab84edaacb094ca34e2bb78c4b75098c3452be4","target":"record","created_at":"2026-05-18T00:53:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4ce4564bf6902f6c5d452f3b1b7a246e42cd39ec4b0f013aecf1b16ed8991dce","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T13:22:00Z","title_canon_sha256":"f6601860629fdf61163c1a6d216ad8dc4ebf5d356359c7559eb3bda413819b29"},"schema_version":"1.0","source":{"id":"1701.01827","kind":"arxiv","version":1}},"canonical_sha256":"6e47a3742f11441ad37a2659bc1ed4cf03aa58632441a2c8817f94159b307905","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e47a3742f11441ad37a2659bc1ed4cf03aa58632441a2c8817f94159b307905","first_computed_at":"2026-05-18T00:53:13.348745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:13.348745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AXwmLrGLUNVpk863HIaMVsFw1iOtvHgeNHjICU/NXPRquWxtZnTl5GG+6zYpv2EZijwuWzbYYv5UBYhMkoPzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:13.349444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75a99b4d6a39c7a2ca3bb0206ab84edaacb094ca34e2bb78c4b75098c3452be4","sha256:46c818366b2307e6f87f5dac25d767e6b241304dd4a8fe4975bab27e5a7af345"],"state_sha256":"081f3afab93d82bbd9cb62c0dca824fa5355bcd06cbf64d730743c01c98d12a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"atB2/sEJkvjKNZLH6xbnJtP5noSZbRPG2qgrQtYN6LKR/2SRirTX5fmeM1+5LNqAtLABgo2YpwlfLyhmkJ5pBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:32:48.433920Z","bundle_sha256":"2d86146ed075720f2f7297e4a3a631c49266fa4292b731e86221fac4aac8ed9c"}}